问题描述:
美国数学竞赛题(都英语进)
1.Make two random marks on a long stick.
(a) If you then break the stick into k pieces of equal length,what's the chance the two marks are on the same piece?
(b) If you then break the stick into k pieces of random lengths,what's the chance the two marks are on the same piece?
2.Leonhard has ten rods having lengths 1,2,...,10 respectively.How many different ways are there to make a triangle by choosing three appropriate rods?
3.A point is chosen randomly inside a square of side length 5,and a unit circle is drawn with that point as its center.Calculate the probability that the circle does not intersect either of the square's diagonals or any of its sides.
4.Circles A,B and C with radii 2,4,and 6 respectively are tangent to one another.The common external tangent to circles A and B intersects the common external tangent to circles A and C at point x.Find the measure of angle x.
5.In the complex plane,let u and v be two distinct solution of .Find the probability that .
1.Make two random marks on a long stick.
(a) If you then break the stick into k pieces of equal length,what's the chance the two marks are on the same piece?
(b) If you then break the stick into k pieces of random lengths,what's the chance the two marks are on the same piece?
2.Leonhard has ten rods having lengths 1,2,...,10 respectively.How many different ways are there to make a triangle by choosing three appropriate rods?
3.A point is chosen randomly inside a square of side length 5,and a unit circle is drawn with that point as its center.Calculate the probability that the circle does not intersect either of the square's diagonals or any of its sides.
4.Circles A,B and C with radii 2,4,and 6 respectively are tangent to one another.The common external tangent to circles A and B intersects the common external tangent to circles A and C at point x.Find the measure of angle x.
5.In the complex plane,let u and v be two distinct solution of .Find the probability that .
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